Extended saddlepoint methods for credit risk measurement

Abstract

We propose a new method that extends the saddlepoint approximation to allocate credit risk. This method applies a Taylor expansion to the inverse Laplace transform around an arbitrary point to characterize the loss distribution of a portfolio. It is based on Hermite polynomials. From a computational point of view, our method is less demanding than other approximate methods. We also extend the current saddlepoint methods to deal with random recoveries and market valuation. Considering a portfolio that includes Spanish financial institutions, we show that these extensions can characterize the risk of the portfolio very well. The risk allocation method generates more accurate results than other approximate methods, with few calculations for default mode models and pure macroeconomy driven recoveries. We also find that modeling mixed idiosyncratic and macroeconomic random recoveries does not generate much greater risk than a pure macroeconomic random recoveries model. Finally, the results for the market valuation approximation are also very accurate, but this method requires a higher number of calculations. Other methods, such as the Monte Carlo importance sampling one, may be more suitable.